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### Uniform Beam Hinged Fixed Ends Natural Frequency Calculator

Natural Frequency of Uniform Beam with Hinged Fixed Ends Equation and Calculator

Eq. 1 Uniform Beam 2 Nodes Clamped Ends

$\omega}_{1}=\frac{15.4}{{L}^{2}}\sqrt{\frac{EIg}{w}$Eq. 2, 3 Nodes

$3.24\cdot {\omega}_{1}$Eq. 3, 4 Nodes

$6.76\cdot {\omega}_{1}$Where:

E = Modulus of elasticity lbs/in^{2}

I = Area moment of inertia, in^{4}

w = weight per unit area of plate, lbs/in^{2}

L = length, in

g = 386, in/sec^{2}

Figure 1, Uniform Cantilever Beam

Source

Bell Helicopter Structural Design Manual, 1977

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